Low-temperature dynamical structure factor of the two-leg spin-$\frac{1}{2}$ Heisenberg ladder

We determine the dynamical structure factor of the two-leg spin-$\frac{1}{2}$ Heisenberg ladder at low temperatures in the regime of strong rung coupling. The dominant feature at zero temperature is the coherent triplon mode. We show that the line shape of this mode broadens in a nonsymmetric way at finite temperatures and that the degree of asymmetry increases with temperature. We also show that at low frequencies, a temperature-induced resonance akin to the Villain mode in the spin-$\frac{1}{2}$ Heisenberg Ising chain emerges.

Figure 1

Exchange couplings for a spin-ladder system. In the strong rung coupling limit, $J_{\parallel }⪡J_{\perp }$.

Figure 2

(Color online) The interband transition for $\left(Q_{\parallel },Q_{\perp }\right)=\left(\pi ,\pi /2\right)$ found by exact diagonalization of a $J_{\parallel }=0.25J_{\perp }$ ladder system of $L=8$ rungs. The thermal broadening is much greater than $\eta =0.01$.

Figure 3

(Color online) The interband transition for $\left(Q_{\parallel },Q_{\perp }\right)=\left(\pi ,\pi /2\right)$ and $L=1000$ sites. The asymmetry grows as $T$ increases.

Figure 4

(Color online) The resummed interband transition line shape for $T=0.4J_{\perp }$, $Q_{\perp }=\pi /2$, $Q_{\parallel }=\pi$, $\eta =0.01$, and $L=1000$ together with a Lorentzian best fit demonstrating the asymmetric line shape.

Figure 5

Dependence of the interband transition at $T=0.5J_{\perp }$ on $Q_{\parallel }$. $Q_{\perp }$ is fixed at $\pi /2$ and $L=1000$. The graphs are offset by $n$ for $Q_{\parallel }=n\pi /4$.

Figure 6

(Color online) A comparison of the resummed spectral function for $T=0.4J_{\perp }$, $Q_{\perp }=\pi /2$, $Q_{\parallel }=\pi$, $\eta =0.02$, and $L=1000$ to the ED result for a $L=8$ system.

Figure 7

(Color online) The intraband transition at a series of temperatures. $Q_{\perp }=\pi /2$, $Q_{\parallel }=\pi$, $\eta =0.01$, and $L=1000$.